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Why the cigar cannot be isometrically immersed into the 3-space
This article has been retracted


Authors: Li Ma and Anqiang Zhu
Journal: Proc. Amer. Math. Soc. 144 (2016), 2619-2622
MSC (2010): Primary 53C44, 32Q20, 58E11
DOI: https://doi.org/10.1090/proc/12973
Published electronically: December 21, 2015
MathSciNet review: 3477079
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Abstract:

The article "Why the cigar cannot be isometrically immersed into the 3-space" by Li Ma and Anqiang Zhu (Proceedings of the American Mathematical Society 144 (2016), no. 6, 2619-2622) is retracted by the author on May 17, 2016 due to mathematical errors detected by the author at a later stage. The article was not withdrawn because of any errors or technical problems found by the reviewers or editors.

In this paper, we study the question if there is an isometric immersion of the cigar soliton into $ R^3$. We show that the answer is negative. This gives a counterexample to the classical Weyl problem on $ R^2$. A similar result in higher dimensions is also true for steady Bryant solitons.


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Additional Information

Li Ma
Affiliation: Department of Mathematics, Henan Normal University, Xinxiang, 453007, People’s Republic of China
Email: lma@tsinghua.edu.cn

Anqiang Zhu
Affiliation: Department of Mathematics, Wuhan University, Wuhan, 430072, People’s Republic of China
Email: aqzhu.math@whu.edu.cn

DOI: https://doi.org/10.1090/proc/12973
Keywords: Weyl problem, cigar soliton, Bryant soliton, isometric immersion
Received by editor(s): July 14, 2015
Published electronically: December 21, 2015
Additional Notes: This research was partially supported by the National Natural Science Foundation of China (No.11271111) and (No.11301400)
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society

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